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So .
(This is Cantor's "diagonal argument").
So louis vuitton alma tasche i the cardinality of R is not. Cantor called it c (except that the symbol should be in copperplate typeface !) the "cardinality of the continuum".
1. The cardinality of A is so there are many transcendentals (in fact c of them !).
2. If is the power set of S then the cardinality of is strictly greater than that of S.
If S is the louis vuitton purse repair atlanta cardinality of S then is 2S. the set of subsets of N is and =, so >.
Hence we get a hierarchy of cardinals :
there is no "largest" cardinal.
3. = c.
He also considered a list of infinite cardinals :
where each is the smallest cardinal which is strictly greater than.
He asked : "Is equal to c?" but could not find the answer.
Nowadays " = c" is called the "continuum hypothesis" and can be taken as an axiom of set theory. (It cannot be proved or disproved from the other set theory axioms).
Cantor also introduced ordinal numbers a generalisation of our :
1st, 2nd, 3rd, 4th,. etc
to louis vuitton shoes ladies infinite ordinals :
.,, +1, +2,.,,.,,.,,.,,.,,.

with strange properties like :
1+ =, +1 ; 2 =, 2 : etc
Some mathematicians (Kronecker, Poincare ) ridiculed this work of Cantor. Others ( Zermelo, Fraenkel, Russell, Hilbert ) thought it brilliant, and sought to base the whole of pure maths on a system of axioms for set theory. This was complicated louis vuitton shoes black by paradoxes which emerged in the theory.

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